In Class Examples of Problems in Kinematics and Dynamics

Last revised 1999/09/29

(a) A 5.00 kg sled is pulled to the right by a 10.0 N force. There is also a frictional force (necessarily to the left). If the block accelerates at 1 m/sec² , how large is the frictional force?
(b) Now suppose a 60 kg person stands on the sled, and the external force is increased enough to maintain the same acceleration. What forces act on the person, and how large are they?
If a car can accelerate from 0 to 15 km/h in 3.0 s, how steep a hill can it climb? Neglect friction.
A 35 kg child is playing on a swing attached to 4.0 m ropes. What force is exerted on the child by the swing at the bottom of its path, if the velocity at that point is 5.0 m/s?
What is the force that must be exerted on each foot of a 90-kg person who has jumped from a height of 3 m in order to stop his fall while he remains on his feet? Assume that his center of mass moves a distance of 0.6 m during his deceleration.
The maximum safe speed of a highway curve can be increased by banking the curve: putting the outer side of the road at a higher level than the inner side. For a curve whose radius is 500 ft, made of a material which has a coefficient of static friction in contact with rubber of 0.50, what is the maximum possible safe speed that can be arranged by adjusting the angle of the banking? The curve must not be so heavily banked that a car at rest would slide off the road!
How fast does a raindrop fall? The retarding force exerted by the air on a raindrop is given approximately by F = bv² with b=4.7x10^-6 N s² /m² and the mass of a raindrop is about 6.5x10^-5 kg.
(a) How much force is required to tow a car at constant speed through loose sand if the effective coefficient of kinetic friction is 0.4?
(b) How much force is required to start the towing job if all four wheels must be started up a slope of sand of 45 degrees and friction can be neglected at this stage of the operation. The tow rope must remain horizontal. Use 1300 kg for the mass of the car.
If a rotary ride has a radius of 4.3 m (14 ft), and the material along the sides has a coefficient of static friction of about 0.55, what must the angular velocity [ d(theta)/dt ] of the ride be so as to just keep the occupants from falling out of the ride? If you were designing the ride, would you use exactly this value?
How much farther could you throw a softball at the equator than at the pole? Neglect any temperature effects, assume the earth to be exactly spherical, and express your answer as a fraction of the distance you could throw the ball at the pole.